Rewrite as a simplified fraction. ${2.\overline{38} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 238.3838...\\ 1x &= 2.3838...\end{align*}}$ Subtracting the two equations, we have: ${99x = 236}$ ${x = \dfrac{236}{99}} \text{or} {2 \dfrac{38}{99}}$